“Both?” Jennifer had asked the developmental pediatrician when, in 2006, the 3-year-olds were diagnosed with autism spectrum disorder. But, honestly, she already knew. Among her teaching credentials was special education certification. Her darling boys were textbook cases. They hadn’t reached for objects, rolled over or sat up at the expected times. As toddlers, they overturned their toy cars and riding toys and spun the tires endlessly, hour after hour, both zoning out, hypnotized.When excited, they jogged in place, flapping their hands above their shoulders like hummingbirds.

Mike did not already know. He’d barely heard of autism. He thought it meant “mental retardation.” Did it mean they were becoming the people about whom others joshed: The elevator doesn’t reach the top floor? The lights are on but nobody’s home?

But once they started walking, the little boys followed their father on silent feet as he stripped floors and spackled walls and replaced wiring in their fixer-upper of a house. There were lulls in their self-stimulating behaviors when Mike took out his tools. They tracked the screwdriver or drill in his hand — from toolbox to task and back. The tools acted like magnets on the boys’ eyes; the eyes silently slid, like nickels along a slot, following the arc of the tools’movements. When Sam Schwenker applied his mechanical intuition to filming his favorite thing — sock puppets — on his parents’ cellphones and Ben Schwenker applied his mechanical sixth sense to undoing his father’s barriers and locks, Mike knew they took after him. The lights were on and somebody was home.

Dr. Leslie Rubin, director of developmental pediatrics at the Morehouse School of Medicine and former director of developmental pediatrics at Emory University School of Medicine, diagnosed the boys. He encouraged Mike and Jennifer to love the children, to treat them as normally as possible, and to stimulate them with every possible experience. “There is no telling what they might achieve,” he said.

But keeping the boys enriched, stimulated and safe was a tall order. Ben, like an estimated half of young children on the autism spectrum, is a “runner” or an “eloper.”

Where is Ben right now? his parents asked themselves with every breath. If one checked an iPhone,the other watched Ben. If one stood at the stove to cook, the other watched Ben. When Mike went out to work, Jennifer watched Ben all day. But, once in a great while, when they both looked down simultaneously at their phones, or let their thoughts drift outside the locked-up house, or Jennifer sagged into the sofa on an interminable afternoon and closed her eyes for a moment, Ben made his move.

“You can be a few feet from him and he gets away,” Jennifer told me. “He watches your gestures and intentions. He studies the whole situation, like a squirrel figuring out how to get in your bird-feeder.”

In the blink of an eye, the scrawny kid perched on an upstairs windowsill, screwdriver in hand,liberating himself. He dropped to the ground — his thin flop of straight brown hair ballooning briefly in the air — and took off across the backyard, pulling off his clothes as he ran. He scaled the tall wooden backyard fence that had been built to corral him and his brother. Naked, he disappeared into a no-man’s-land of fields, subdivisions, strip malls and state routes.

Typical of children with autism, Ben ran first toward the glitter of water. He stripped as he ran and leapfrogged fences because, regardless of the season, he planned to go swimming.

He skinny-dipped as the uninvited pool guest of some unknown neighbor, climbed out, and found his way into the house. He wanted to examine wiring, HVAC units, laundry vents, attic fans, and pipes.

Neighbors were mystified. Then a local couple nearly tripped over the culprit: They came in one night to find a skinny, wet, naked little white boy sprawled out on their kitchen floor with his head inside the cabinet under the sink. He appeared to be studying the garbage disposal unit. They yelped and demanded an explanation,but the boy ran away. They pursued him out the door and soon came across the Schwenkers, jogging down the road and calling, “BEN!”

Far worse for the Schwenkers were the times that no neighbor emerged with a complaint. Then Mike and Jennifer froze in the driveway, not knowing which way to run first, willing themselves not to hear a squeal of tires in the distance or the revving-up whoop of a siren. They tottered about — a few steps this way, a few steps that way — looking at each other with stricken faces. They dialed 911. The universal parental monotone prayer-to-avert-disaster moved on their lips: Please please please please or Oh God oh God oh God.

Mike worked long hours at Delta, including nights, weekends, 12-hour shifts. Other than the few hours per day the boys went to school (to special ed classrooms from which they came home frazzled and incoherent), Sam and Ben and Jennifer stayed sealed up in the silent house on the quiet street.

Locked inside the house all day, the boys “stimmed” (self-stimulated through repetitive movements), kicked, pinched, licked or slapped each other; they literally bounced off the walls. Jennifer fell into silence and claustrophobia; she was deeply alone. Though she resisted, she sometimes gave in to moments of weeping— alone in the bathroom, hiding her distress from the boys. There were days she hardly combed her hair or put on an attractive pair of slacks. Every expert agreed that the boys needed real-life adventures and experiences outside the house. But it mostly fell to Jennifer to take them.

The boys’ favorite outing was to Best Buy. Sam, ever on the lookout for puppets, pulled his mom toward the big-screen televisions in case “Sesame Street” was on, while Ben was desperate to reach the appliances. When Mike was available, they made good use of their time by splitting into teams of two. But when Jennifer, because they had to go somewhere, took the boys alone, she could end up shipwrecked: arms outstretched in the midst of the cellphone department as Ben tried to tow her toward Large Appliances, and Sam threw his weight into dragging her to TV & Home Theater.

And it did no good then to ask herself, What was I thinking? because she knew she had thought: If we don’t leave the house today, I will lose my mind. Of course by then they were becoming a public spectacle — both boys beginning to freak out, to squeal, to fall down and rage, squirming across the tired carpet, each in his longed-for direction.

It was a rare excursion that ended peacefully. By the time she staggered, dragging them, back across a parking lot, her hair was undone, her face red, her dress askew, and the boys were wailing and unhinged, their brief joy turned to confusion.

“I’m actually turning into a shut-in,” Jennifer told her husband as gently as possible, at a moment she thought he could bear to hear it. “I can’t hardly leave the house. I can’t hardly stay home anymore. It’s like I keep thinking: This is my life.” She followed up with a soft laugh.

They couldn’t afford a nanny; she knew they couldn’t. They couldn’t afford a babysitter. They couldn’t afford private school or private tutors. And there was no end in sight— not high school graduation, not college graduation, not young adulthood, not marriage, at least not at the rate they were going.

Jennifer researched autism endlessly. She joined online associations of “autism parents.” In early 2009, when the twins were 6, she read about a child showing improved day-to-day functioning with an “autism assistance dog.” She was intrigued and mentioned it to Mike. They loved dogs. Could this be an option for them?

❏ ❏ ❏

Every month, roughly after a year of waiting and fund-raising, a dozen families pull up in rental cars from the Dayton or Cincinnati airport or in wheelchair-accessible vans filthy from cross-country trips. Xenia, Ohio, is a leafy antebellum village, a former safe haven on the Underground Railroad. A few blocks from downtown, on three acres of land, sits the former VFW hall, an aluminum-sided one-story rectangular building. It’s a modern dog-training academy now.

In the parking lot, the families unload their gear: little crutches or small motorized wheelchairs; walkers and gait trainers; aerosol equipment like breathing machines, mouthpieces, masks and suction pumps; apnea monitors; floor mats and wedges; feeding tubes, feeding bags, and powdered formula; commode chairs,catheters and diapers from small to adult sizes.

The arriving families are white, African-American, Asian and multiracial. Deeply weary — and not just from the journey from across the United States and from a few foreign countries — these are people whose lives revolve around keeping “special needs” children alive, and safe. In some families, a child’s lifelong crisis began with an accident or with the onset of a disease; for some, it was a genetic syndrome confirmed soon after birth; for others, there were red flags during pregnancy; and for others, a child by adoption began to reveal issues for which the parents felt unprepared.

Many families include siblings of the special needs child, often too young to understand why they never get to be the center of attention and why even the new dog will not be theirs.

Some of these families have been cheated by unscrupulous operators. Service dog training is an unregulated industry. “There’s no national standard, no national certification, and no guide to reputable agencies,” Karen Shirk, 52, the founding director of 4 Paws, told me. “We end up picking up the pieces.”

Wheeling, carrying, coaxing, dragging or chasing their children across the gravel parking lot toward the double glass doors, many parents experience a sudden flash of hope. No one is unreservedly optimistic. Everyone is well acquainted with cycles of optimism, disappointment, exhaustion and despair. But as they spy handsome dogs frolicking on green acreage beyond the fence, some permit themselves the thought: This is one crazy idea that just might work.

Photo: Jennifer and Michael Schwenker use a service dog, Barkley, to help control their twins, Ben and Sam, who have autism. Sam has progressed to the point that he doesn’t need to be tethered in most situations, but Ben, a risk of running off, still does.

For the Schwenker twins, Jeremy had chosen the bloodhound/Lab mix and trained him in autism assistance, tracking and tethering. If Ben got away, Barkley would pursue him.But as long as Ben was clipped to Barkley, his chances of escape would be greatly diminished.

On the family’s first field trip in Xenia with Barkley, the great gleaming beast compliantly waited beside the 4 Paws van in a shopping mall parking lot while three leashes were attached to his harness: one sloped up to Jennifer and two hung sideways to the kids. Mike prepared to follow behind. Then the Schwenker family — like four planets in orbit around a shiny black sun — marched into the mall.

Tethered to Barkley, the boys tripped and tangled and double-stepped down the wide polished foyers. They seemed unaware of the fact that they were now — like water-skiers— being towed. If they tried to dash away, Barkley, like a puttering motorboat, churned forward and tugged them back into place.

After a few days of practice on the daily field trips, the children weren’t just stumbling alongside their ox-like friend, they were putting out their hands, patting his broad back and hanging on to his tail, almost as if they’d always known him. Ben, naturally, was interested in the mechanics of the thing. He liked to raise the flaps of Barkley’s ears to peer inside, and when the great dog yawned, Ben positioned himself to get the long view straight down the throat.

Back in Atlanta, Jennifer prepared for outings like a parachutist confirming every strap and rope before stepping into the air. It took a while to get the leashes and clips right; Ben mastered them instantly, escaped from the rigging, and ran away, but finally his mother outwitted him with a heavy-duty locking carabiner. He might get away from her but he would not get away from Barkley.

It was embarrassing, at first, to step into public. “We were a total spectacle, like a traveling circus act,” Jennifer told me. “People would stop to look at us while one of the kids who’s not paying attention walks smack into a post and then we’re trying not to clothesline people, catching them in the middle of a long leash.” At the center of the moving maypole plodded Barkley, his droopy bloodhound ears swinging, his droopy bloodhound eyes bright and amused. Her awareness that they were semi-ridiculous faded. And sometimes people who felt obliged to comment on her family — “You sure do have your hands full!” or “What’s wrong with them?” — offered positive remarks instead, like “What a beautiful dog.” Jennifer’s career as a shut-in was at an end.

Four days after moving to Atlanta with his new family, Barkley alerted Mike and Jennifer to a jailbreak. He barked, bucked and charged about restlessly at the back door and,sure enough, Ben was gone. They released Barkley outdoors with the command: “Find Ben!” and he instinctively ran through the three phases of tracking: He roamed in wide half-circles looking for the freshest traces of Ben (Search phase), slowed down and moved several paces along an invisible path (Deciding phase), then locked in and sped up, nose down, after the boy (Decision phase).

The career of the Cobb County Neighborhood Intruder had also come to an end.

From the forthcoming book “The Underdogs: Children, Dogs and the Power of Unconditional Love” by Melissa Fay Greene. Copyright @ 2016 Melissa Fay Greene. To be published May 17 by Ecco, an imprint of HarperCollins Publishers. Excerpted by permission.